border-image is tied to the border-width. It's possible to use the offset to choose the amount of the image to show from the origin (i.e. topoffset of 10px + border-top-width of 10px will show 10px from pixel 0 to pixel 10).

But if you use a border-width of 0px instead, it's possible to use the offset to hide a portion of the image. In this case you can use padding to achieve the same alignment as with border-width.

See this post (where I was corrected by Scott Murray, thanks Scott) for more info and demo: